Elders are often portrayed as wise and age is seen as a indication of knowledge when looking at past cultures. Is there any proof that people in ancient times suffered from disorders like Alzheimers or Dementia?

Mental "decay" on account of old age is referenced in the writings of quite a few ancient sources. Just about every introduction to dementia I've seen makes some passing mention to Plato, Aristotle or even Pythagoras with theories of life stages involving the loss of mental faculties or memory in old age. Irritatingly, they seem to almost never provide sources!

At any rate, here is a translated document that comes to us from Cicero. Among other things, he gives us what is in fact an impassioned defense of the mental faculties of the elderly, presenting a "if you don't use it, you lose it" line of thought:

But, it is said, memory dwindles. No doubt, unless you keep it in practice, or if you happen to be somewhat dull by nature. Themistocles had the names of all his fellow-citizens by heart. Do you imagine that in his old age he used to address Aristides as Lysimachus? For my part, I know not only the present generation, but their father, also, and their grandfathers. Nor have I any fear of losing my memory by reading tombstones, according to the vulgar superstition. On the contrary, by reading them I renew my memory of those who are dead and gone. Nor, in point of fact, have I ever heard of any old man forgetting where he had hidden his money. They remember everything that interests them: when to answer to their bail, business appointments, who owes them money, and to whom they owe it. What about lawyers, pontiffs, augurs, philosophers, when old? What a multitude of things they remember! Old men retain their intellects well enough, if only they keep their minds active and fully employed. Nor is that the case only with men of high position and great office: it applies equally to private life and peaceful pursuits. Sophocles composed tragedies to extreme old age; and being believed to neglect the care of his property owing to his devotion to his art, his sons brought him into court to get a judicial decision depriving him of the management of his property on the ground of weak intellect—just as in our law it is customary to deprive a paterfamilias of the management of his property if he is squandering it. Thereupon the old poet is said to have read to the judges the play he had on hand and had just composed—the Oedipus Coloneus—and to have asked them whether they thought that the work of a man of weak intellect. After the reading he was acquitted by the jury. Did old age then compel this man to become silent in his particular art, or Homer, Hesiod, Simonides, or Isocrates and Gorgias, whom I mentioned before, or the founders of schools of philosophy, Pythagoras, Democritus, Plato, Xenocrates, or later Zeno and Cleanthus, or Diogenes the Stoic, whom you too saw at Rome? Is it not rather the case with all these that the active pursuit of study only ended with life?

This is significant because it is an acknowledgement from the classical period that it is not a universal phenomenon to experience a decline later in life. That he was arguing this case at all lends credence to the existence of some kind of widespread belief that extreme old age came with it a risk (or perhaps certainty) of senility.